1. Field of the Invention
The present invention relates to an ion implantation process simulation device realizing accurate interpolation and extrapolation of ion implantation profiles including tails in ion implantation process simulation for a semiconductor device, and a simulation method therefor.
2. Description of the Related Art
A manufacturing process of semiconductor devices including LSI includes a step of implanting impurity ions as dopant into a semiconductor substrate by an ion implantation technique and diffusing and activating them through a thermal treatment. It is well-known that an impurity distribution obtained in this step accounts for the considerable change in a threshold voltage Vt, an ON-state current of a transistor and other electrical characteristics parameters. In recent years, in particular, for reducing a semiconductor in size to achieve high density large capacity and high speed, designing a transistor with shallower junctions has been gaining more importance. More specifically, demanded is not only accurate control of a peak concentration of impurities but also accurate adjustment of position of the tail of an ion implantation profile.
In order to meet this demand, ion implantation process simulation using a computer is adopted. This is a method of predicting and calculating various ion implantation profiles for use in manufacturing semiconductor devices by using predetermined models and algorithms on a computer. Use of ion implantation process simulation largely contributes to the reduction in the number of experimental steps for improving element characteristics of a semiconductor device and to the improvement in efficiency of designing work.
In simulating ion implantation profiles, in general, ion implantation profiles are described using a Gaussian or Pearson function which can obtain satisfactory enough approximation when crystals are amorphous. At that time, since ion implantation into a semiconductor crystal substrate reflects crystallinity of the substrate, profiles will vary depending on crystal orientation of the substrate and an ion implantation angle, that is, the channeling phenomenon will occur. The channeling phenomenon tends to decrease with an increase in dose value. This is because crystals become amorphous as a dose value is increased. Profiles of ion implantation into a semiconductor crystal substrate can not therefore be described by using a simple Gaussian or Pearson function but can be described by using a plurality of functions.
A technique of describing a profile of ion implantation into a semiconductor crystal substrate by using a function and simulating the same is disclosed, for example, in "An Improved Approach to Accurately Model Shallow B and BF.sub.2 Implants in Silicon" (Al F. Tasch, H. Shin, and C. Park; J. Electrochem. Soc., Vol. 136, No. 3, March 1989, pp. 810-814; The Electrochemical Society, Inc.). The literature recites a method of more accurately simulating experimental profiles of as-implanted ion impurities. The experimental profiles are results of measurement obtained by the SIMS (Secondary Ion Mass Spectrometry) method. SIMS is a well-known method of irradiating a surface region of a semiconductor with a primary ion such as an oxygen ion or a cesium ion to generate a secondary ion and conducting mass analysis of the secondary ion to measure an impurity distribution. The experimentally obtained ion implantation profile is expressed using two Pearson functions which represent an amorphous component and a channeling component, respectively. The ion implantation profile N(x) is described as a sum of the two components as shown in the following equation (1). EQU N(x)=D.sub.main f.sub.main (x)+D.sub.sub f.sub.sub (x) (1)
where a main peak amorphous component function f.sub.main (x) and a subsidiary peak channeling component function f.sub.sub (x) are normalized functions not dependent on a dose value, while D.sub.main represents a main peak amorphous component dose coefficient and D.sub.sub represents a subsidiary peak channeling component dose coefficient. A total dose D.sub.T of the ion implantation profile N(x) is described as a sum of coefficients of the amorphous component dose and the channeling component dose as shown in the following equation (2). ##EQU1## The Pearson function used here is described using four kinds of moment parameters, projected range Rp, standard deviation .DELTA.Rp, skewness .gamma. and kurtosis .beta..
In the following, description will be made of a conventional ion implantation process simulation method of obtaining an ion implantation profile for a prescribed dose by interpolation, with reference to a flow chart of FIG. 6. With reference to FIG. 6, first, from table data of ion implantation profiles for several dose values, extract moment parameters, projected range Rp, standard deviation .DELTA.Rp, skewness .gamma. and kurtosis .beta. in two normalized functions respectively representing the amorphous component and the channeling component (moment parameters of a Dual Pearson function), an amorphous component dose coefficient and a channeling component dose coefficient (Step 601). As a result, a Dual Pearson data table is prepared. Next, select parameters for doses at two points most neighboring to an arbitrary dose from the Dual Pearson data table (Step 602). Next, out of the selected parameters, linearly interpolate the dose-dependent amorphous component dose coefficient and channeling component dose efficient with respect to dose (Step 603).
More specifically, first, use SIMS experimental profile data at a plurality of dose points to extract a functional parameter value and a ratio of the coefficients of an amorphous component dose at a main peak to a total dose, D.sub.main /D.sub.T. The functional parameter and the ratio of the coefficients of an amorphous component dose at a main peak to a total dose are recited for boron and BF.sub.2 in the above-described literature.
FIG. 7 is a diagram showing a dose dependency as a parameter to be interpolated. In FIG. 7, the abscissa represents a dose value, the ordinate represents a main peak amorphous component dose ratio and the polygonal line represents a dose dependency of a main peak amorphous component dose ratio. As illustrated in FIG. 7, the number of dose points of the experimental data shown in the diagram are five, not so many. Ratios of the coefficients of a main peak amorphous component dose to the total dose at the other doses need to be interpolated for all the doses. When moment data and ratios of coefficients of a main peak amorphous component dose to the total dose (D.sub.main, i /D.sub.T, i) and (D.sub.main, i+1 /D.sub.T, i+1) of the ion implantation profile at dose values D.sub.T, i and D.sub.T, i+1 of two points for the interpolation or extrapolation with respect to an arbitrary dose value D.sub.T, a are given, linear interpolation by a conventional simulation method will result in describing a ratio of each coefficient of the amorphous component dose and the channel component dose to the total dose at the arbitrary dose value D.sub.T, a, that is, (D.sub.main, a /D.sub.T, a) and (D.sub.sub, a /D.sub.T, a), as shown in the following equation (3). ##EQU2##
According to the above-described conventional ion implantation process simulation method, however, when profiles N.sub.i (x) and N.sub.i+1 (x) at two dose points D.sub.T, i and D.sub.T, i+1 (D.sub.T, i &lt;D.sub.T, i+1) satisfy the relationship N.sub.i (x)&lt;N.sub.i+1 (x), inversion might occur between the intensity of a profile N.sub.a (x) obtained by linear interpolation with respect to a dose point D.sub.T, a located between the two points and the intensity of the profile N.sub.i+1 (x). Shown in FIG. 8 as an example are calculation results obtained by a standard process simulator SUPREM-3 which is widely used at present. With reference to FIG. 8, the curve CP3 of the profile N.sub.a (x) obtained by linear interpolation between the profile curves CP2 and CP4 according to the above-described conventional linear interpolation method crosses with the profile curves CP1 and CP2 for larger doses at the tail. In other words, the profile curve CP3 is undesirably shown to have a higher concentration than those of the profile curves CP1 and CP2.
Based on this result, it is possible to conduct interpolation with respect to a logarithmic value of a dose on the abscissa according to the following equation (4). ##EQU3## While the interpolation results obtained in this case are slightly improved as compared with those of FIG. 8, undesirable inversion of the intensity at the tail can not be avoided.
As described in the foregoing, conventional ion implantation process simulation methods have a drawback that in simulation of an impurity profile for junction depth, undesirable interpolation is caused at a tail of the ion implantation profile to prevent acquisition of accurate simulation results.